Question

You and your spouse have found your town home in San Marcos, CA. The selling price is $360,000; you will put $60,000 down and obtain a 30–year fixed-rate mortgage at 7.25% for the rest.

3. Refer to above.

Assume that monthly payments begin in one month. What will each payment be?

A. $2,325.01

B. $2,046.53

C. $1,876.48

D. $1,938.72

E. $2,173.46

4. Refer to above. Although you will get a 30-year mortgage, you plan to prepay the loan by making an additional payment each month along with your regular payment. How much extra must you pay each month if you wish to pay off the loan in 20 years? (Hint: first, compute the monthly payments as if it were a 20 year-year loan, then calculate the difference)

A. $548.38

B. $413.75

C. $383.62

D. $276.34

E. $324.67

5. Refer to above. Your banker suggests that, rather than obtaining a 30-year mortgage and paying it off early, you should simply obtain a 15-year loan for the same amount. The rate on this loan is 7%. By how much will your monthly payment be (higher/lower) for the 15-year loan than the regular payment be (higher/lower) for the 15-year loan than the regular payment on the 30-year loan?

A. Lower; $311.57

B. Lower; $554.72

C. Higher; $485.26

D. Higher; $647.58

Answer 1

1)

Loan principal = House price - Downpayment

Loan principal = $360,000 - $60,000

Loan principal = $300,000

no of periods = 30 years * 12 = 360 months

Monthly payment for a 30 year loan

Monthly payment = Loan principal * (interest rate / 12) / (1 - (1 + (interest rate / 12))^{-no of periods})

Monthly payment = $300,000 * (7.25% / 12) / (1 - (1 + (7.25% / 12))^-360)

Monthly payment for a 30 year loan = $2046.53

2)

no of periods = 20 years * 12 = 240 months

Monthly payment for a 20 year loan

Monthly payment = Loan principal * (interest rate / 12) / (1 - (1 + (interest rate / 12))^{-no of periods})

Monthly payment = $300,000 * (7.25% / 12) / (1 - (1 + (7.25% / 12))^-240)

Monthly payment for a 20 year loan = $2371.13

Difference to be paid = Monthly payment for a 20 year loan - Monthly payment for a 30 year loan

Difference to be paid = $2371.13 - $2046.53

Difference to be paid = $324.6

You will have to pay additional $324.6 in each monthly payments to pay off the loan.

3)

Monthly payment for a 20 year loan at 7% interest rate

Monthly payment = Loan principal * (interest rate / 12) / (1 - (1 + (interest rate / 12))^{-no of periods})

Monthly payment = $300,000 * (7% / 12) / (1 - (1 + (7% / 12))^-180)

Monthly payment for a 20 year loan = $2696.48

Difference in loan monthly payment = Monthly payment for a 15 year loan at 7% interest rate - Monthly payment for a 30 year loan at 7.25% interest rate

Difference in loan monthly payment = $2696.48 - $2046.53

Difference in loan monthly payment = $649.95

You will have to pay additional (Higher) $649.95 in each monthly payments to pay off the loan.